Q.A bar magnet of dipole moment $\vec{m}$ is placed in a uniform magnetic field $\vec{B}$ making angle $\theta$ with it. Derive the expression for the torque acting on the magnet, and write the expression for its potential energy in this orientation.

A short bar magnet placed in a uniform external magnetic field $\vec B$ experiences a torque $\vec\tau=\vec m\times\vec B$, of magnitude $\tau=mB\sin\theta$, where $\vec m$ is the magnet's dipole moment and $\theta$ is the angle between $\vec m$ and $\vec B$. This is exactly the same result derived earlier for a current-carrying coil in a uniform field, applied here to a bar magnet: the forces on its two poles are equal in magnitude, act along different (parallel) lines through the two poles, and so form a couple. Because the two pole forces are equal and opposite, they cancel to give zero NET force in a uniform field -- only a pure rotational torque results, which tends to rotate the magnet until $\vec m$ is aligned with $\vec B$. …